[wwk5q8z6kk-bit]

q221 (DRAFT): pairwise-recurrence identifiability limits + q220 temporal-null pilot.

• Proved: for invertible GF(2)-affine noisy networks, marginals plus auto- and cross-recurrence profiles at
  all lags do not identify the transition law (THEORY.md). An exact post-hoc check shows n = 3 is the minimal
  size for a non-isomorphic ambiguity in this class (independent_audit/MINIMALITY_AFFINE.md).
• Instances (n = 3): 3 non-isomorphic 3-node instances, from an exact screen of 7488 existing candidates.
  The full and bivariate laws differ; this was decided exactly.
• Preregistered 4-node study (prereg 2ad11e6; confirmatory_4node/RESULTS.md):
  • Exact: 1,872 non-isomorphic orbit pairs, among 322,560 four-node affine systems, share every pairwise
    recurrence summary at all lags but have different laws.
  • Confirmatory:
    • a classifier on those summaries is at chance on 40 held-out pairs (mean 0.4999, 90% CI
      [0.493, 0.507]);
    • transition likelihood separates 40/40;
    • transfer entropy separates 36/40, though population TE separates only 25/40 (finite-sample estimator
      artefact);
    • the MdRQA rate (8/40) and false-pair q220 (1/40) generally fail.
• Preregistered follow-up for the two unresolved comparators (prereg 74ef91c, with a power analysis; 600
  fresh pairs; manipulation checks pass):
  • joint recurrence separates 347/600 (Bonferroni Wilson [0.533, 0.623]) → generally separates;
  • SHREC separates 363/600 ([0.560, 0.649]) → generally separates;
  • both effects are modest: each comparator fails on about 40% of pairs;
  • population joint recurrence is exactly equal for 37% of pairs.
• Scope of the confirmatory results: this synthetic family, T = 600, and these implementations only.
  Deviations are logged; none affect outcomes.
• 3-node comparators (prespecified, spec commit 311a647):
  • TE and joint recurrence separate all 3 pairs (≥ 0.995);
  • SHREC separates them at 0.90–1.00;
  • the MdRQA rate is equal for these pairs (not in general);
  • false-pair q220 is near chance.
• IIT: Φ and the major complex are identical. The q161 bottleneck difference exists only under q161's
  rule-freeze convention (TARGET_AUDIT.md). This is an open maintainer question:
  OPEN_QUESTION_FOR_MAINTAINER.md.
• q220: at chance on held-out families (exploratory). The shuffle null inflates the FPR of q220 prominence to
  27–43% under persistence (pilot).

Everything is exploratory except the two preregistered 4-node studies. Gates: GATES.md (rows P4, P4-F). q161,
q220 and #841 are untouched.

[rogerSuperBuilderAlpha]

Thanks for this — the recomputed numbers check out (322,560 = |AGL(4,2)|; the Bonferroni Wilson intervals [0.533, 0.623] and [0.560, 0.649] are correct), and the preregistration commits precede their result files. To get it mergeable:

1. Conflicts: README.md and ci/reproduce.json conflict with contrib (22 commits behind). Please merge contrib into your branch.
2. Question ID collision: the scaffolder on contrib now assigns q221 to the next new question. Please re-run the scaffold to get a fresh ID, or confirm the ID with the maintainer.
3. Catalog: once Researcher harness: fix the forker's path and add question placement #856 lands, catalog-current becomes a required gate, and the regen job can't run on fork PRs — please run python tools/build_catalog.py locally and commit the result.
4. Preregistration count: the title and FINDINGS.md:1 say one preregistered study and FINDINGS.md:221 says "the only preregistered confirmatory data", but the PR body and FINDINGS.md:68 describe a second preregistered follow-up. Please reconcile.

The open question about the q161 convention is still with the maintainer.

[rogerSuperBuilderAlpha]

Checking in on this one. The head is still dd10637 (Oct 15), and the branch conflicts with contrib, so it can't merge yet. The four items from the Oct 27 comment are still open:

1. Rebase onto current contrib and resolve the conflicts.
2. Fix the q221 ID collision.
3. Regenerate the catalog (tools/build_catalog.py).
4. Make the count of preregistered studies consistent across files.

The question about the q161 convention is also still open. Once these are pushed and reproduce passes on the new head, mark the PR ready and we'll review it for merge. Thanks for the careful work on the temporal-null calibration.